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2019

Ultimate tensile deformation and

strength capacity of shear tab connections

Zhang, Chen

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Ultimate Tensile Deformation and Strength Capacity of Shear Tab

Connections

by

Chen Zhang

A thesis

submitted to the Faculty of Graduate Studies

in partial fulfillment of requirements for the

Degree of Master of Science

in

Civil Engineering

Supervisor

Yanglin Gong, Ph.D., P.Eng.

Professor, Dept. of Civil Engineering

Co-Supervisor

Jian Deng, Ph.D., P.Eng.

Associate Professor, Dept. of Civil Engineering

Lakehead University

Thunder Bay, Ontario

June 2019

© Chen Zhang, 2019

ii

Declaration I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including

any required final revisions, as accepted by my examiners. I understand that my thesis may be

made electronically available to the public.

iii

Abstract Single plate or shear tab is a common simple connection to connect steel beams to columns. The

connection is traditionally designed for the shear load transferred from the supported beam only,

while it has long been recognized that the shear connection can resist a certain amount of tensile

force in the longitudinal direction of the supported beam which is critical to preserve the integrity

of a structure. Canadian standard CSA/S16-14 explicitly states that connections shall be designed

to provide resistance to progressive collapse as a consequence of a local failure. However, few

specific design requirements are provided in the standard. Hence, the main objective of this

research is to quantify the deformation and strength capacities of shear-tab connections when

subjected to a pure tension or a combined tension and shear load in the context of progressive

collapse resistance.

First, a set of full-scale shear tab connection specimens were tested under a pure tension load.

The results from the experiments are then used to verify and calibrate a finite element model of

the connections. Thirdly, the finite element model is used to conduct a parametric study to

determine the impact of tab thickness, tab edge distance, bolt diameter and the combined effect of

tension and shear load. Finally, a formulation describing the relationship between the tensile force

and the axial deformation for the shear tab connections is developed.

iv

Acknowledgements This research would not be successful without the help of many people that I owe a debt of

gratitude. I would like to express my gratitude to all those who helped me during the course of this

thesis.

First, my deepest gratitude goes to Professor Yanglin Gong, my supervisor, for his constant

encouragement and guidance. Dr. Gong has walked me through all the stages of this research.

Without his patient instruction, insight criticism and expert guidance, the completion of this thesis

would not have been possible. Also, I would like to thank my co-supervisor, Professor Jian Deng,

whose support, knowledge and experience helped me tremendously during the research.

I would like to thank Professor Sam Salem for serving as a thesis committee member. My

gratitude is also due to Professor Hao Bai for serving as the external thesis examiner.

I would like to thank students Blake Peters, Daniel Leung, Thomas Wipf and Asparukh

Akanayev, for assistance in executing the laboratory work. Thank you for spending your reading

week by my side at Lakehead University Structure Laboratory.

I would like to extend my appreciation to my parents who gave me their love and support

throughout my studies. Last, but not least, a special thanks to my fiancée, with her support, patience

and understanding throughout this research, I have completed this thesis.

v

Contents Abstract ………………………………………………………………………………..…………iii

Acknowledgements …………………………………………………………...………………….iv

Contents …………………………………………………………………………………...............v

List of Tables ………………….………………………………………………………………...viii

List of Figures ……………...……………………………………………………………………..ix

Chapter 1 Introduction ………………………………………………………….……….1

1.1 Research consideration and objectives …………………………………………………….1

1.2 Lab tests of shear tab connection ……………………………..……………………………3

1.3 Finite element modeling of shear tab connections ………………………………...……….9

1.4 Design guideline for shear tab connections ………………………………………………12

1.5 Thesis Outline ……………………………………………………………………………..13

Chapter 2 Experimental test ……………………………………………………..……..14

2.1 Test setup and design ……………………………………………………………………...14

2.2 Test procedure ……………………………………………………………………………..22

2.3 Test results …………………………………………………………………………………23

2A Appendix Coupon test ……………………………………………………………………..33

Chapter 3 Finite element modeling ……………………………………………….……38

3.1 Modeling process ………………………………………………………………………….38

3.1.1 Generating the geometry …………………………………………………………….38

3.1.2 Inputting material property ………………………………………………………….40

3.1.3 Assembly ……………………………………………………………………………50

3.1.4 Setting analysis step …………………………………………………………………51

3.1.5 Applying interaction ………………………………………………………………...51

3.1.6 Applying load ……………………………………………………………………….52

3.1.7 Mesh design …………………………………………………………………………53

3.1.8 Job …………………………………………………………………………………..53

3.1.9 Visualization ………………………………………………………………………...54

3.2 Simulation results …………………………………………………………………………54

T95-45-1 …………………………………………………………………………………..54

T95-57-1 …………………………………………………………………………………..55

vi

T127-45-1 ……………………………………………………………………………........56

T95-45-2 …………………………………………………………………………………..57

T127-45-2 ……………………………………………………………………………........58

3.3 Comparison ……………………………………………………………………………….59

T95-45-1 …………………………………………………………………………………..59

T95-57-1 …………………………………………………………………………………..59

T127-45-1 ……………………………………………………………………………........60

T95-45-2 …………………………………………………………………………………..60

T127-45-2 ……………………………………………………………………………........61

3.4 Summary ………………………………………………………………………………….61

Chapter 4 Parametric study ……………………………………………………………62

4.1 Parameters ………………………………………………………………………………...62

4.2 Simulation results of 19mm bolt diameter ………………………………………………...62

T95-38-1 ……………………………………………………………………………..........63

T95-48-1 ……………………………………………………………………………..........64

T64-38-1 ……………………………………………………………………………..........65

T64-48-1 ……………………………………………………………………………..........66

T127-38-1 …………………………………………………………………………………67

T127-48-1 …………………………………………………………………………………68

4.3 Simulation results of 22.2mm bolt diameter ………………………………………………68

T64-45-1 …………………………………………………………………………………..69

T64-57-1 …………………………………………………………………………………..70

T127-57-1 …………………………………………………………………………………71

4.4 Simulation results of 25.4mm bolt diameter ………………………………………………71

T95-51-1 …………………………………………………………………………………..72

T95-64-1 …………………………………………………………………………………..73

T64-51-1 …………………………………………………………………………………..74

T64-64-1 …………………………………………………………………………………..75

T127-51-1 …………………………………………………………………………………76

T127-64-1 …………………………………………………………………………………77

4.5 Simulation results of combined tension and shear …………………………………..……..77

vii

4.6 Observations ………………………………………………………………………………79

Chapter 5 Analysis of the load versus deformation curve …………………………….80

5.1 The method of a tri-linear curve …………………………………………………………...80

5.2 Determination of Ty and Δy ………………………………………………………………...81

5.3 Determination of Tu and Δu ………………………………………………………………..85

5.4 Determination of Tr and Δr ………………………………………………………………...91

Chapter 6 Conclusions and future works …………………………………………..….95

6.1 Summary and conclusions ………………………………………………………………...95

6.2 Future works ……………………………….……………………………………………...96

References ……………………………………………………………………………………....97

viii

List of Tables

Table 1.1 Results of 11 shear tab connection tests …………………………………………………7

Table 1.2 Summary of the FE simulation results by Ashakul (2004) …………………………….10

Table 2.1 Shear tab specimen matrix ……………………………………………………………..17

Table 2.2 Shear tab connection specimens ………………………………………………...……..17

Table 2.3 List of bolts and coupons (bolt diameter=7/8 in) ………………………………….……20

Table 2.4 Strength and failure modes of tested specimens ……………………………………….24

Table 2.5 Results of deformations ………………………………………………………………..26

Table 2.6 Measurement of each coupon ………………………………………………………….34

Table 2.7 Yield strength and ultimate strength of coupons ……………………………………….37

Table 3.1 The dimensions of 5 parts of specimen T95-45-1 in Abaqus ………………………….40

Table 3.2 True stress, strain and engineer stress, strain (T95 models) ……………………….......41

Table 3.3 True stress, strain and engineer stress, strain (T127 models) ………………………….43

Table 3.4 Calibration results of the fracture initiation for T95 models …………………………...47

Table 3.5 Calibration results of the fracture initiation for T127 models …………………………48

Table 3.6 Mesh design of each part ………………………………………………………………53

Table 3.7 Simulation results of lab tests ……………………………………………………….....58

Table 3.8 Summary of the simulation results in comparison with the predicted and test

results …………………………………………………………………………………………....61

Table 4.1 The summary of failure modes of the 18 simulation …………………………………...79

Table 5.1 Summary of 6 lab tests and 15 simulations …………………………………………….82

Table 5.2 Calculation results of the 10 lab tests ………………………………………………….86

Table 5.3 Calculation results of the 15 simulations ………………………………………………87

Table 5.4 Determination of the ultimate deformation ……………………………………………89

Table 5.5 Calculation results of Equation (5.13) and (5.14) ……………………………………...91

Table 5.6 Determination of Tr …………………………………………………………………....92

Table 5.7 Determination of Δr ………………………………………………………………..…..93

ix

List of Figures

Figure 1.1 Two types of shear tab connection ……………………………………………….…….2

Figure 1.2 Lipson’s test setups …………………………………………………………………….4

Figure 1.3 Guravich and Dawe’s test setup ………………………………………………….…….6

Figure 1.4 Thompson’s test setup ……………………………………………………………...…8

Figure 1.5 Oosterhof and Driver’ s test setup …………………………………………………..….9

Figure 1.6 Daneshvar and Driver’s finite element model ………………………………………...11

Figure 1.7 Final deformed shape of the finite element model …………………………….………11

Figure 2.1 The test setup on universal testing machine …………………………………….…….14

Figure 2.2: Test setup for pure tension …………………………………………………………...15

Figure 2.3: Design of shear tab specimens ……………………………………………………….16

Figure 2.4: Upper arm drawing ……………………………………………….………….………18

Figure 2.5: Lower arm ………………………………………………………………….………..19

Figure 2.6: Measurement of Δ ……………………………………………………………………21

Figure 2.7 Photos of specimens T95-45-1-a and T95-45-2-b …………………………………….23

Figure 2.8 Failure modes ………………………………………………………………………...25

Figure 2.9 Deformation sources …………………………………………………………….…....26

Figure 2.10 Load-deformation curve of T95-45-1-a ………………………………………….….27

Figure 2.11 Load-deformation curve of T95-45-1-b ………………………………………….…28

Figure 2.12 Load-deformation curve of T95-57-1-a …………………………………………….28

Figure 2.13 Load-deformation curve of T95-57-1-b ………………………………………….….29

Figure 2.14 Load-deformation curve of T127-45-1-a ……………………………………………29

Figure 2.15 Load-deformation curve of T127-45-1-b ……………………………………………30

Figure 2.16 Load-deformation curve of T95-45-2-a ……………………………………….…….30

Figure 2.17 Load-deformation curve of T95-45-2-b ………………………………………….….31

Figure 2.18 Load-deformation curve of T127-45-2-a ……………………………………………31

Figure 2.19 Load-deformation curve of T127-45-2-b ……………………………………………32

Figure 2.20 Coupon size………………………………………………………………………….33

Figure 2.21 Coupon setup and photos after test …………………………………………….…….34

Figure 2.22 Load-position curve of coupon 1 ……………………………………………………35


x




Figure 3.1 Modeling process in Abaqus ………………………………………………………….38

Figure 3.2 The quarter model …………………………………………………………………….39

Figure 3.3 Five parts of finite element modelling …………………………………………….….40

Figure 3.4 Engineer stress, strain and true stress, strain for T95 models …………………..……42

Figure 3.5 Engineer stress, strain and true stress, strain for T127 models ……………………….44

Figure 3.6 Evolution of stress triaxiality in the critical finite element (bearing tear-

out) ………………………………………………………………………………………………46

Figure 3.7 Evolution of stress triaxiality in the critical finite element (net-section

rupture) …………………………………………………………………………………………..46

Figure 3.8 Stress triaxiality vs. fracture strain for T95 models ……………………………….....47

Figure 3.9 Stress triaxiality vs. fracture strain for T95 models ……………………………..…...48

Figure 3.10 Stress-strain curve with progressive damage degradation ………………………….49

Figure 3.11 Definitions of damage evolution based on plastic displacement (linear) ………..….50

Figure 3.12 The analysis model in Abaqus …………………………………………………….…50

Figure 3.13 The position of bolt ………………………………………………………………….51

Figure 3.14 Surface 1 …………………………………………………………………………….52

Figure 3.15 Surface 2 …………………………………………………………………………….53

Figure 3.16 Spectrum of stresses ………………………………………………………………...54

Figure 3.17 Load-deformation curve of T95-45-1 ……………………………………………….54

Figure 3.18 Deformation shapes of T95-45-1 ……………………………………………………55


Figure 3.20 Deformation shape of T95-57-1 ……………………………………………….…….56

Figure 3.21 Load-deformation curve of T127-45-1 ……………………………………………...56

Figure 3.22 Deformation shape of T127-45-1 ……………………………………………………56


Figure 3.24 Deformation shape of T95-45-2 ……………………………………………….…….57


Figure 3.26 Deformation shape of T127-45-2 ……………………………………………………58

xi

Figure 3.27 Specimen T95-45-1 …………………………………………………………………59


Figure 3.29 Specimen T127-45-1 ………………………………………………………………..60


Figure 3.31 Specimen T127-45-2 ………………………………………………………………..61

Figure 4.1 Combined tension and shear force ……………………………………………………62

Figure 4.2 Load-deformation curve of T64-38-1 ………………………………………………...63

Figure 4.3 Final deformed shape of T64-38-1 ……………………………………………………63




Figure 4.7 Final deformed shape of T95-38-1 ……………………………………………...……65

Figure 4.8 Load-deformation curve of T95-48-1 ………………………………………….…......66



Figure 4.11 Final deformed shape of T127-38-1 …………………………………………………67




Figure 4.15 Final deformed shape of T64-45-1 …………………………………………….…….69







Figure 4.22 Load-deformation curve of T64-64-1 …………………………………………….…73

Figure 4.23 Final deformed shape of T64-64-1 ……………………………………………….….73

Figure 4.24 Load-deformation curve of T95-51-1 …………………………………………….…74



xii

Figure 4.27 Final deformed shape of T95-64-1 ……………………………………………….….75





Figure 4.32 Load vs. deformation of T95-45-1 under combined tension and shear ………….…78

Figure 4.33 Failure modes of T95-45-1 under combined tension and shear ………………….....78

Figure 5.1 Tri-linear curve of T95-45-1 ………………………………………………………….80

Figure 5.2 Load versus deformation of a nonlinear spring ………………………………………81

Figure 5.3 Determination of Ty …………………………………………………………………..83

Figure 5.4 Determination of Ky …………………………………………………………………..84

Figure 5.5 Block shear failure ……………………………………………………………………85

Figure 5.6 Determination of ∆u …………………………………………………………………..90

Figure 5.7 Determination of Tr …………………………………………………………………...92

Figure 5.8 Determination of Δr …………………………………………………………………..94

Figure 6.1 Failure modes when V 0.45T ………………………………………………………..96

1

Chapter 1 Introduction

This chapter provides a general background about shear tab connections and the reasons of this

study. Research objectives and literature review are listed, and the outline of the thesis is presented.

1.1 Research considerations and objectives

Shear tab connection is one of the most popular and common simple connections used in steel

construction industry because of its cost efficiency, easy fabrication, and rapid erection capabilities.

It usually consists of a single steel plate and several bolts to connect a beam to a column or a girder.

The connecting plate is welded to the supporting member in shop, while the connection between

the supported beam and the steel plate is achieved with the use of bolts on site. There are two kinds

of shear tab connections: one is called the shear tab connection (or the conventional shear tab

connection), the other is the extended shear tab connection. Figure 1.1 shows the two types of

shear tab connections for beam-to-column and beam-to-girder joints.

(a) shear tab connection

2

(b) extended shear tab connection

Figure 1.1 Two types of shear tab connections

Shear connections of steel structures are traditionally designed for the shear load transferred

from the supported beam only, while it was long been recognized that these shear connections can

resist a certain amount of tensile force in the longitudinal direction of the supported beam. This

tensile force resistance allows the development of a horizontal tying force (called catenary action)

which helps to preserve the integrity of the structures. In Canada, the steel structure standard

CSA/S16-14 (CSA 2014) explicitly states that connections shall be designed to provide resistance

to progressive collapse as a consequence of a local failure (Clause 6.1.2). However, few specific

design requirements are provided in the standard. Instead, the standard states that “the

requirements of this standard generally provide a satisfactory level of structural integrity for steel

structures”.

Recent research found that when assessing the integrity of a steel structure against progressive

collapse, the scenario of a sudden column loss could impose a very large tension force on the shear

connections, as the girders or beams need to structurally span two bays under the sustained gravity

loads. Thus, the modeling of steel connections under a tensile load is essential for evaluating the

behaviors of a steel structure under such an abnormal loading.

The main objective of this research is to develop formulas to predict the deformation and

strength capacities of conventional shear tab connections subjected to a tension load. In order to

achieve this goal, we need to finish the sub-objectives as follows:

1) A set of experimental tests are conducted to quantify the ultimate strength and deformation

3

capacities of shear tab connections subjected to a pure tension load.

2) The results from the experiments will be used to verify a finite element model of the

connections.

3) The finite element model will be used to conduct a parametric study.

4) Finally, a formulation describing the relationship between the tensile force and the tensile

deformation of the shear tab connections will be developed.

1.2 Lab tests of shear tab connection Lipson (1968) conducted a study on the performance of three kinds of simple connections,

including the welded bolted single plate which is now commonly referred to as a shear tab. The

shear tab was welded to a supporting beam and bolted to the web of the supported beam .

A single vertical row of bolts (2 to 6 A325 bolts) were used for a series of 12 full-scale tests.

Three types of loading were conducted: pure moment, moment-shear with no rotation, and

moment-shear with rotation. Figure 1.2 shows the two setups in the study.

4

Figure 1.2 Lipson’s test setups (Mirzaei, A., 2014)

In Figure 1.2(a), the two test beams were spliced together in the middle at the point of zero shear,

and for the setup in Figure 1.2(b) , two hydraulic jacks were used to control rotation.

The purposes of the Lipson’s work were to observe the behavior of shear tab connections under

the loads, to find the maximum rotational capacities of the connections, to determine a safety factor

for the ultimate load, and to evaluate the feasibility of the shear tabs. Lipson observed three kinds

of failure modes: weld rupture, bolt tear-out and plate yielding. His investigation showed that the

centre of rotation, which was close to the centre of bolt group, was not more than 20mm from the

centre in the direction of the compression edge of the shear tab. Also, the test results showed that

bolt slip occurred at a rotation of less than 0.04 radians. He concluded that it was feasible to use

these connections in reality.

Astaneh et al.(1993) presented a strength-based design guideline for shear tabs, and the

guideline was later adopted by the American Institute of Steel Construction (AISC) manual. There

were 5 strength limits in the guideline: plate yielding, bearing failure of bolt holes, fracture of the

net section of the plate, bolt fracture, and weld fracture. This design approach was applicable with

both ASTM A325 and A490 bolts, either fully tightened or snug tightened. The procedure was not

applicable to oversized or long-slotted bolt holes. The requirements of the guidelines are: the

connection has only one vertical row of bolts, and the number of bolts is not less than 2 and more

5

than 7; bolt spacing is equal to 76 mm; edge distances are equal to or greater than 1.5d, where d is

the diameter of the bolts, and the vertical edge distance for the lowest bolt is preferred not to be

less than 38 mm; thickness of the single plate should be less than or equal to d/2 + 1/16 in; the ratio

of c/d of the plate should be greater than or equal to 2 to prevent local buckling of the plate, where

c is edge distance; the distance between the bolt line and the weld line was limited to 64-76 mm;

the size of the connecting fillet weld was required to be greater than 0.75t, where t is the thickness

of the shear tab.

A series of test specimens was designed with this approach, and the test results showed that the

ductile and tolerated rotations was from 0.026 to 0.061 radians at the point of the maximum shear.

The number of bolts influenced the rotational ductility; i.e., the higher the number of bolts, the

lower the rotational ductility that could be achieved. At last, the experimental studies indicated that

considerable shear and bearing yielding occurred in the plate before the failure. The yielding would

decrease the rotational stiffness which would cause the reduction of the end moments of the

supported beam.

Guravich and Dawe (2006) tested 108 full-scale shear tab connections. Their main goal was to

investigate the performance of shear tab connections under the effect of combined shear, moment

and tension force.

They used a single row of 3 bolts (3/4 inch ASTM A325) to connect the shear tab (7.9mm

thickness), which was commonly used at that time. Figure 1.3 shows the test setup.

6

Figure 1.3 Guravich and Dawe’s test setup (Mirzaei, A., 2014)

Two vertical W310 × 97 reaction columns were fixed to the rigid ground while two horizontal

W610 × 155 reaction beams were framed to the two columns. The upper beam was the support for

cylinder D, and the lower beam acted as a rigid support for the specimens. Shear tabs were welded

to a steel plate which was bolted onto the lower beam. Five hydraulic cylinders were used: A

applied the main shear force to the connection; B and C controlled the rotation of the connection;

D applied the tension force; E controlled the position of cylinder D to keep the force perpendicular

to the beams . The test procedures were as follows:

1) rotated the test beam to 0.03 radians and applied the desired value of shear force (either half

7

or total of the factored bolt shear capacity)

2) applied the axial tension to the test beam (the rotation and shear force remain unchanged

during the testing）

Table 1.1 shows the results of 11 shear tab connection tests.

Table 1.1 Results of 11 shear tab connection tests.

Notes: Vtest: Applied shear load; Tult: ultimate tension load; Vres: Resultant shear force; Bp: Bearing resistance of shear tabs.

From Table 1.1, T308-1 and T308-2 failed with plate buckling failure under pure shear load, and

all other tests failed with steel plate shear fracture. Also, from the average ratio of Vres/Bp of 0.94,

they concluded that Bp was a key factor to determine the ultimate resistance capacity of shear tab

connection under combined shear and tension load.

Thompson (2009) investigated 9 full-scale tests of shear tab connections under a scenario of

column removal. His main goal was to determine the stability of the shear tab connections and

their ability for the catenary action. Figure 1.4 shows the test setup.

8

Figure 1.4 Thompson’s test setup (Mirzaei, A., 2014)

Two identical shear tabs were connected to the test beams in the middle of the setup. The other

ends of the test beams were pin-connected to the frame columns. A hydraulic cylinder below the

test specimen was used to apply a force to the shear tab connections .

The test results gave three failure modes: bolt shear, localized net section tensile rupture, and

localized block shear rupture at the bottom bolt location. Thompson concluded that the shear tab

connections had the ability to resist the unexpected forces because of the loss of a column.

Oosterhof and Driver (2011) tested 45 full scale specimens of various kinds of simple

connections, including 9 shear tabs, under combined shear, moment and axial forces to simulate a

column removal scenario.

Two kinds of shear tab specimens were used: a 230 x 110 x 6.4 mm shear tab connected by three

19.05mm diameter ASTM A325 bolts to a W310x143 test beam; a 390 x 110 x 9.5 mm shear tab

connected by five 22.2mm diameter ASTM A325 bolts to a W530 x 165 test beam. Figure 1.5

shows the test setup.

9

Figure 1.5 Oosterhof and Driver’s test setup (Mirzaei, A., 2014)

The setup was different from Thomson’s (2009), as it only used one test beam and one shear tab

connection on a W250x89 test column. Three actuators were used to apply any combination of

shear, moment and axial forces to the connection. Actuators 1 and 2 applied the moment and shear,

while actuator 3 applied the axial force.

Oosterhof and Driver’s connection rotation reached 0.08 to 0.13 radians. They observed that the

tear-out of bolt was a main failure mode for the shear tab connections.

1.3 Finite element modeling of shear tab connections

Ashakul (2004) used software Abaqus to simulate the lab test of Astaneh et al. (1989) and Sarkar

(1992). The simulation included two types of shear tabs: single-row and double-row of shear tabs.

Ashakul created 12 finite element models in the research, including 8 models stemmed from

Astaneh et al. and Sarkar’s lab test, 2 models for showing the effect of the size and length of the

test beams, and another two models for investigating the influence of loading type and bolt strength.

Table 1.2 shows the summary of the study .

10

Table 1.2 Summary of the FE simulation results by Ashakul (2004)

As shown in Table 1.2, the finite element models had a fair accuracy in predicting the ultimate

resistance of the connections, though most of the results were overestimated by the models.

Ashakul claimed that the reason why some of the results were 20 percent larger was that the bolt

was in the shear plane. Furthermore, Ashakul used 42 finite element models to conduct a

parametric study which included 4 variables: “a” distance between the bolt and the welded line,

plate thickness, material of the plate, and single or double row shear tabs.

Ashakul’s findings were:

1) “a” distance had no effect on bolt shear rupture resistance;

2) the ductility criteria couldn’t use for connections, and the connections created high horizontal

forces in bolts which would reduce the shear resistance of the bolts. Also , there was a moment

created by those forces which should be considered in design.

3) in a double row thick plate shear tab connection, the second row (from the support base)

resisted most of the stresses, and the first row had very small forces.

4) if the strain hardening performed, the shear stress distribution did not remain unchanged

through the cross section of the plate.

Daneshvar and Driver (2011) used software Abaqus to simulate 9 lab tests by Thomson (2009).

Figure 1.6 shows the model in the software.

11

Figure 1.6 Daneshvar and Driver’s finite element model

The loading was treated as a displacement assigned to the interior column. Figure 1.7 shows the

final deformed shape of the finite element model.

Figure 1.7 Final deformed shape of the finite element model

From the models, one can see that the shear tab connections had a high ductility capability

12

because of the bearing located around the bolt holes. Daneshvar and Driver concluded that the

hardest part of simulation in Abaqus was the nonlinearity definition.

Henning Levanger (2012) used software Abaqus to simulate ductile fracture in steel and

compared two models for describing local instability because of ductile fracture. The first model

used material’s true stress and strain relationship for reducing load-bearing capacity to get the

ductile fracture of the material; the other model was based on the assumed energy for forming a

crack, and reduced the load-bearing capacity by giving damage to the elements of the model.

Alireza Mirzaei and co-researchers (2014) did a series of full-scale lab tests of shear tab

connections and used Abaqus to mimic the performance of these shear tab connections. A series of

four full-scale tests were performed on shear tab connections between a W610x140 beam and a

W360x196 column, as well as a W310x60 beam and a W360x196 column. The shear tab, which

was configured as a double bolt row connection, was subjected to a combined vertical (shear) force

and axial tension along with the anticipated rotation of a typical beam-to column joint. A matching

specimen was then tested under shear and axial compression. The results from these tests and

previous shear tabs tested under gravity load alone were used in the development of a finite element

model that was capable of simulating the response of the connection under shear load and

predicting the ultimate resistance and the progression of failure. The models presented in the thesis

featured special modelling techniques and were able to predict all types of failure modes such as

bearing, net area fracture, shear yielding, flexural yielding, and weld tearing of the connections.

Next, the FE models were used to investigate the performance of shear tabs subjected to

combined shear and axial force. Shear force–axial force interaction curves were generated for

various levels of axial tension and compression force for twelve connections. At last, a design

approach was proposed which allowed practicing engineers to include the effect of any axial force

level in the design of a shear tab connection.

1.4 Design guideline for shear tab connections

The current design procedure for shear tabs in the CISC Handbook of Steel Construction (2016)

is based on the research carried out by Astaneh et al. (1989). Table 3-41 in the Handbook presents

the factored resistances of shear tabs with one vertical row of 2 to 7 bolts connected to rigid

supports (such as the flange of a W section column) or flexible supports (e.g. the web of a column

or a girder) by using E49 fillet welds and diameters ½”, ¾”, 20 mm and 22 mm A325 bolts. The

13

methodology behind the values listed in the table is as follows: 1) determine the effective

eccentricity for the bolt group based on Astaneh et al’s (1989) research; 2) find the single plane

shear resistances of the bolts used; 3) determine the thickness of the shear tab plate; and 4) choose

the weld size to fully develop the shear tab. The current Canadian approach does not cover the

usage of multiple vertical rows of bolts or the use of more than 7 bolts per row. The size and

thickness of the shear tab is also limited due to restrictions largely based on the original scope of

test specimens. It also does not address the application of an axial force on the connection.

1.5 Thesis outline

Chapter 2 presents laboratory test of 10 shear tab connections under a pure tension load. The test

design, setup, procedures and results are discussed in detail.

Chapter 3 describes the finite element modeling of the tested connection specimens using

software Abaqus 6.14. The finite element model is calibrated with the experimental results.

Chapter 4 presents a parametric study of the shear tab connections by using the finite element

model established in Chapter 3. The design parameters include tab thickness, edge distance, bolt

diameter, and the combined effect with shear force.

Chapter 5 proposes a load-deformation curve for the shear tab connections from the elastic stage

to the damage stage.

Chapter 6 states the conclusions from this research, and provides some recommendations for

future works.

14

Chapter 2 Experimental test

In this chapter, the details of the lab test of 10 shear tab connections under a pure tension load are

presented.

2.1 Test setup and design

The tension test was conducted on a SATEC 500 kips (2225 kN) universal testing machine. Figure

2.1 shows a picture of the setup in lab. Figure 2.2 shows the design of the setup, which consisted

of one upper loading arm, one lower loading arm, and a specimen between the loading arms. The

design of the shear tab specimen is shown in Figure 2.3. The loading arms were fixed to the loading

heads of the universal testing machine by clamping (Figure 2.4 and Figure 2.5). Figure 2.6 shows

the measurement of displacement.

Figure 2.1 The test setup on universal testing machine

15

Figure 2.2 Test setup for pure tension

Measurements: 1) tension force T 2) elongation Δ

lower arm

tension

50

tab plate, fillet welded to anchor plate 116

anchor plate, 50 mm thick

300

126

220

185

Unit: mm

16

anchor plate, 215×200×50

Figure 2.3 Design of shear tab specimens

215

200

116

76 62 62

tab plate, thickness 9.5 or 12.7

a=80

50

c= 45 (or 57)

200

76 38 38

Top View

Front View of One-Line Specimen

Front View of Two-Line Specimen

tab plate, thickness 9.5 or 12.7

a=80

50

45

200

76 38 38

76

Unit: mm

17

In this project, we have three kinds of test variables: 1) tab plate thickness t . Use two thicknesses:

9.5 mm and 12.7 mm; 2) tab edge distance c. Use two distances: 45 mm and 57 mm; 3) number of

columns of bolts. Use two patterns: one line only, and two lines.

The size of the fillet welds between the shear tab plate and the anchor plate is (5/8)t. Tables 2.1

shows the specimen matrix. Ten specimens were tested in total (Table 2.2).

Table 2.1: Shear tab specimen matrix One-line specimen Two-line

specimen, Edge c=45 mm

Bolt length (mm) Edge c=45 mm

Edge c=57 mm

4 tension bolts

2 or 4 shear bolts

Tab thickness t=9.5 mm 2 2 2 108

(41/4 in) 108 (41/4 in) Tab thickness

t=12.7 mm 2 2

Table 2.2: Shear tab connection specimens Shear Tab Specimen ID

Tab thickness t (mm)

Edge distance c (mm)

One- or two-column lines

Note

T95-45-1-a 9.5 45 1 The first T95-45-1-b 9.5 45 1 The second T95-57-1-a 9.5 57 1 The first T95-57-1-b 9.5 57 1 The second T95-45-2-a 9.5 45 2 The first T95-45-2-b 9.5 45 2 The second T127-45-1-a 12.7 45 1 The first T127-45-1-b 12.7 45 1 The second T127-45-2-a 12.7 45 2 The first T127-45-2-b 12.7 45 2 The second

Note: T=shear Tab; followed by thickness, 95=9.5 mm; 127=12.7 mm,; followed by c; followed by number of rows of bolts; and a is the first of the kind, and b is the second of the kind. For example, specimen T95-45-1a had a tab thickness of 9.5 mm, edge distance of 45 mm, one-column of bolts, and the first specimen of the kind. Specimen T127-45-2b had a tab thickness of 12.7 mm, edge distance of 45 mm, two-column of bolts, and the second specimen of the kind.

18

Figure 2.4 Upper arm drawing

228

70

40

fillet welds between P1 and P2: 12 mm all around

23.8 holes

plate P2, 375×228×19

300

126

220

185

70

190

6×38

76

T-shape plate P1, 25mm thick

Unit: mm

19

260 mm

260

Figure 2.5 Lower arm

300

stiffener 15 mm thick

260x200x25 plate

200

126

PL2

76 62

PL2

g2=45

45

76 62 62

100

250 120 80

100

PL3

PL3

Top View of Lower Arm

Side View of Lower Arm

Front View of Lower Arm

Design of lower arm: (1) lower arm: the g2 gauge is 45 mm. (2) PL2 welded to PL3 using complete penetration

groove weld (3) stiffeners welded to PL2 using complete

penetration groove weld; and to PL3 using 10 mm fillet welds

(4) PL1, PL2 and PL3 have thickness of 25 mm (5) Bolt hole diameter 23.8 mm

37

Unit: mm

20

Four bolts (of ASTM A490, diameter of 7/8 inch) were used to fasten the specimen to the lower

loading arm. Two ASTM A490 high-strength bolts of 7/8 inch diameter were used to connect the

specimen to the upper loading arm. Bolt hole diameter is 23.8mm. The lower and upper arms were

re-used throughout the test. Table 2.3 shows the list of bolts and coupons.

Table 2.3: List of bolts and coupons (bolt diameter=7/8 in) Category Item Number Bolts A490 , length=4 in

A490 , length=41/4 in 56 (The tension bolts will be re-used)

Shear tab plate coupons

6 coupons in total; each thickness 3 coupons of 30 mm × 300 mm

The connection design (Figure 2.3) adopted typical North American practice. The tab plate was

welded to a 50 mm thick anchoring plate, which was in turn fastened to the lower loading arm

during test. The tab materials were CSA/G40.21 300W steel. Their measured strengths were: yield

strength Fy=376 MPa and ultimate tensile strength Fu=490 MPa for 9.5 mm thick tab; Fy=387 MPa

and Fu=495 MPa for 12.7 mm thick tab (Appendix 2A). The sizes of the welds and bolts were

chosen based on a capacity design principle such that rupture failures of the welds and bolts would

not occur during the test.

21

Figure 2.6 Measurement of Δ

Measurements: 1) tension force T 2) elongation Δ

lower arm

Tension T

116

g1

126mm

Δ of tab

4 linear potentiometers, 2 each side, are used to measure Δ, elongation of a tab under tension.

22

2.2 Test procedure

Before starting, measure dimensions of the test arms, check if they match design dimensions. All

the shear tab specimens shall be measured and photoed before testing. Photos shall be taken with

the tab placed on a clean background (a white color board as background). When taking photos,

always include a printed label showing the ID of the connection.

The test procedures are as follows:

1) place the lower arm onto the Universal Testing machine.

2) install shear tab specimen, and snug tighten the tension bolts.

3) place the upper loading arm. Install and snug tighten shear bolts.

4) take photos of the connection, with printed lab of ID.

5) install displacement gauges.

6) check data acquisition system.

7) set up safety screen.

8) start loading while recording data. Load the connection to rupture with displacement-

controlled loading.

9) unload.

10) take photos of the connection before taking it off, including printed label ID.

Figure 2.7 shows the photos of two specimens before testing: T95-45-1-a and T95-45-2-b.

23

Figure 2.7 Photos of specimens T95-45-1-a and T95-45-2-b

2.3 Test results

The yield, ultimate and rupture tensile strengths (Ty, Tu, Tr) of each specimen and its corresponding

deformations (Δy , Δu , Δr ) are recorded in Table 2.4. The observed failure modes included bearing

tear-out and net-section rupture which are presented in Figure 2.8.

24

Table 2.4 Strength and failure modes of tested specimens Specimen ID Tensile strengths

Ty, Tu , Tr (kN) Failure mode

T95-45-1a,b 385, 430, 200 Bearing tear-out T95-57-1a,b 376, 488, 270 Net-section rupture T127-45-1a,b 510, 535, 380 Bearing tear-out T95-45-2a,b 440, 480, 105 Net-section rupture T127-45-2a,b 592, 640, 95 Net-section rupture

T95-45-1-a: bearing tear-out T95-45-1-b: bearing tear-out

T95-57-1-a: net-section rupture T95-57-1-b: net-section rupture

T127-45-1-a: bearing tear-out T127-45-1-b: bearing tear-out

25



Figure 2.8 Failure modes

There were four plastic deformation patterns at failure: bearing of hole, bending of hole edge,

shear tearing of hole, and tensile necking. Figure 2.9 shows the measurement of these permanent

deformations. Table 2.5 records the results after measuring the deformations.

26

Figure 2.9 Deformation sources

The permanent plastic deformations were measured as follows:

1) bearing deformation of a hole = (dimension a before test) – (dimension a after test)

2) bending deformation of a hole edge = dimension b

3) Shear tearing deformation of a hole = dimension c

4) Tensile necking deformation = (total deformation) – (hole bearing deformation) – b – c

5) Total plastic deformation = (dimension d after test) – ( dimension d before test)

Table 2.5 Results of deformations Specimen ID Hole

bearing deformation (mm)

Hole bending deformation (mm)

Shear tearing deformation (mm)

Necking (mm)

Total plastic deformation (mm)

T95-45-1a,b 4.0 10.0 4.0 0.0 18.0 T95-57-1a,b 7.0 1.0 0.0 9.0 17.0 T127-45-1a,b 3.0 10.0 3.0 0.0 16.0 T95-45-2a,b 4.0 1.0 0.0 5.0 10.0 T127-45-2a,b 4.0 1.0 0.0 5.0 10.0

a

d

b

c

27

The tensile load T versus deformation Δ curves of the ten specimens are illustrated as following

(Figures 2.10 to 19). Typically, the T-Δ curves had a bolt slippage in the beginning, followed by a

linear elastic stage, then a gradual decrease of stiffness, followed by another linear stage until a

rupture was initiated. Note that the tensile load indicated in the curves is a quarter of the real tensile

load (i.e, ¼ of T ) for the convenience of comparing with the finite element models in Chapter 3.

Figure 2.10 Load-deformation curve of T95-45-1-a

0

10

20

30

40

50

60

70

80

90

100

110

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Load (kN)

Deformation (mm)

T95-45-1-a

28

Figure 2.11 Load-deformation curve of T95-45-1-b


0

10

20

30

40

50

60

70

80

90

100

110

120

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Load (kN)

Deformation (mm)

T95-45-1-b

0

10

20

30

40

50

60

70

80

90

100

110

120

130

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Load (kN)

Deformation (mm)

T95-57-1-a

29



0

10

20

30

40

50

60

70

80

90

100

110

120

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Load (kN)

Deformation (mm)

T95-57-1-b

0102030405060708090

100110120130140150

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Load (kN)

Deformation (mm)

T127-45-1-a

30



0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Load (kN)

Deformation (mm)

T127-45-1-b

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Load (kN)

Deformation (mm)

T95-45-2-a

31



0

10

20

30

40

50

60

70

80

90

100

110

120

130

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Load (kN)

Deformation (mm)

T95-45-2-b

0102030405060708090

100110120130140150160170180

0 1 2 3 4 5 6 7 8 9 10 11 12

Load (kN)

Deformation (mm)

T127-45-2-a

32


0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

0 1 2 3 4 5 6 7 8 9 10 11 12

Load (kN)

Deformation (mm)

T127-45-2-b

33

2A Appendix Coupon test

Tensile coupon tests were used to determine the material’s yield strength, ultimate strength, and

fracture strain. In this study, tensile coupon tests were carried out using Tinius Olsen universal

testing machine.

The coupons (300mm 30mm) were cut from the shear tab plates. The specified material for

shear tab plates was G40.21 300W steel.

Three coupons were cut for 9.5mm thickness tab and 12.7mm thickness tab, respectively. Figure

2.20 shows the dimensions of the coupons.

Test Procedure:

1) measure the length and thickness of the coupons

2) install the coupons to Tinius Olsen universal testing machine

3) install the gauges on the coupon

4) input the essential parameters to the computer

5) start recording data

6) start loading to rupture

7) unload

8) measure the length and thickness of the coupons

Figure 2.21 shows the testing machine with a coupon on it and the coupons after test.

78.7mm

300 mm

Figure 2.20 Coupon size

34

Figure 2.21 Coupon setup and photos after test

The thickness, middle length before and after testing of each coupon were recorded in Table 2.6.

Table 2.6 Measurement of each coupon Coupon ID Thickness (mm) Middle length

(mm) Middle length after test (mm)

elongation

Coupon 1 12.31 7.87 9.87 0.25 Coupon 3 12.29 7.87 9.74 0.24 Coupon 4 9.32 7.87 9.88 0.25 Coupon 5 9.34 7.87 9.81 0.25 Coupon 6 9.42 7.87 9.88 0.26

The load versus position curves of each coupon are given as Figures 2.22 to 26 (unit: lbf, in).

The yielding strength and ultimate strength of each coupon can be obtained from the load vs.

position curves (Table 2.7).

35

Figure 2.22 Load-position curve of coupon 1


36



37


Table 2.7 Yield strength and ultimate strength of coupons Coupon ID

Yield strength (MPa)

Ultimate strength (MPa)

Average of yield strength (MPa)

Average of ultimate strength (MPa)

Coupon 1 380 495 387 495 Coupon 3 394 496 Coupon 4 365 493 376 491 Coupon 5 399 499 Coupon 6 365 481

38

Chapter 3 Finite element modeling

This chapter describes the finite element modeling of the tested specimens, using software Abaqus

6.14. In a finite element analysis, a shear tab is discretized into many small elements, and the

displacements at each node and the stresses within every element are obtained under the applied

load.

3.1 Modeling process

In Abaqus, the modeling process includes 9 main parts: geometry modeling, material property,

assembly, analysis step, interaction, loading, meshing, job and visualization. The relationships

among these parts are shown in Figure 3.1.

Figure 3.1 Modeling process in Abaqus

The following presents each part of the modeling process and the details of the finite element

modeling of a shear tab.

3.1.1 Generate the geometry

In geometry modeling part, Abaqus provides some ways and tools to build every part of the whole

model. Also, it allows to input the geometry parts from a third-party graphic software.

39

In order to reduce computer time, a quarter of the whole specimen is simulated because the

specimen is a bi-symmetry geometry. Figure 3.2 shows the formation of a quarter model.

In Figure 3.2, there are two axes of symmetry in the shear plate. For axis of symmetry 1, the cut

section is just allowed movement in Y-Z plane, and forbid movement in X direction. For axis of

symmetry 2, the cut plane is prohibited movement in Z direction, and can has movement in X-Y

plane. Also, the anchor plate is treated as a fix support and thus omitted in the modeling, and three

geometrical configurations are used to model the weld connection between the shear plate and the

anchor plate.

In total, there are 5 parts which are needed to create a quarter of the whole lab test specimen.

Figure 3.3 shows the 5 parts in Abaqus.

axis of symmetry 1

axis of symmetry 2

axis of symmetry 1

axis of symmetry 2

Figure 3.2 The quarter model

Top view Front view

Top view of a quarter model

axis of symmetry 1

X

Y

Z

40

Figure 3.3 Five parts of finite element modeling

The first one is a quarter of the whole shear tab; the last one is used to simulate the bolt; the

other three parts are combined together into the welding line between the shear tab and the anchor

plate. Table 3.1 shows the sizes of these 5 parts for specimen T95-45-1.

Table 3.1 The dimensions of 5 parts of specimen T95-45-1 in Abaqus Part ID Dimensions (mm) Part 1 76 125 4.75 Part 2 9.5 9.5 76 Part 3 9.5 9.5 4.75 Part 4 9.5 9.5 9.5 Part 5 22.2 14.525

Note: the size of the hole on the shear plate is 23.8mm 9.5mm.

3.1.2 Input material property

The material properties of three stages were needed: elastic, plastic and damage. The yield and

ultimate strengths of steel materials in terms of engineering stress were obtained by coupon tests

41

(see 2A appendix for details).

In elastic stage, 200 GPa and 0.3 for Young’s Modulus and Poisson’s ratio were used. In plastic

stage, the stress and strain are required to be expressed as the true stress and strain instead of

engineering stress and strain. The relationships between true strain, stress and engineering strain,

stress are as follows:

= E (1 + E) (3.1)

and

= ln(1 + E) (3.2)

where and are true strain and stress, respectively; E and E are engineering strain and stress,

respectively.

Table 3.2 and Figure 3.4 show the engineering stress, strain and true stress, plastic strain for T95

models.

Table 3.2 True stress, strain and engineering stress, strain (T95 models) Engineering stress (MPa) Engineering strain True stress (MPa) Plastic strain 376 0.00188 377 0.000 377 0.02900 388 0.027 378 0.03200 390 0.030 425 0.04600 445 0.043 448 0.05900 474 0.055 477 0.08900 519 0.083 486 0.11500 542 0.106 491 0.14500 562 0.133 463 0.25000 579 0.220

Note: in the software Abaqus, the first data of plastic strain is equal to 0, corresponding to the initial yield stress of the material.

42

Figure 3.4 Engineering stress, strain and true stress, strain for T95 models

For T127 models, similar to T95 models, Table 3.3 and Figure 3.5 show the details of stress and

strain relationships.

0

100

200

300

400

500

600

0 0.05 0.1 0.15 0.2 0.25 0.3

Engineering

stress(MPa)

Engineering strain

0

100

200

300

400

500

600

700

0.00 0.05 0.10 0.15 0.20 0.25

True stress(MPa)

Plastic strain

43

Table 3.3 True stress, strain and engineering stress, strain (T127 models) Engineering stress (MPa) Engineering strain True stress (MPa) Plastic strain 387 0.00194 388 0.000 389 0.03200 401 0.030 391 0.03400 404 0.031 446 0.05300 470 0.050 469 0.06900 501 0.064 481 0.09300 526 0.084 489 0.11800 547 0.109 495 0.15400 572 0.140 474 0.25000 593 0.220

Note: in the software Abaqus, the first data of plastic strain is equal to 0, corresponding to the initial yield stress of the material.

0

100

200

300

400

500

600

0 0.05 0.1 0.15 0.2 0.25 0.3

Engineering

stress(MPa)

Engineering strain

44

Figure 3.5 Engineering stress, strain and true stress, strain for T127 models

In damage stage, there are two sections which are required to simulate: ductile damage initial

and damage evolution. For ductile damage initial, the ductile criterion is a phenomenological

model for predicting the onset of damage due to nucleation, growth, and coalescence of voids. The

model assumes that the equivalent plastic strain (fracture strain) at the onset of damage is a function

of stress triaxiality and strain rate. The stress triaxiality (Ravi Kiran and Kapil Khandelwal, 2014)

is defined as the ratio of hydrostatic stress and the Mises stress as follows:

T = σH / σM (3.3)

σH = (σ1+σ2+σ3) / 3 (3.4)

σM = [σ12+σ2

2+σ32- (σ1σ2 +σ2σ3 +σ1σ3)]0.5 (3.5)

where: T=stress triaxiality; σH=hydrostatic stress; σM=Mises stress; σ1, σ2 and σ3 are principal

stresses.

According to Ravi Kiran and Kapil Khandelwal (2014), the stress triaxiality is a key factor to

cause dominant damage of microvoid elongation and dilation, and the stress triaxiality above

which the softening caused by the microvoid dilation exceeds the strengthening caused by the

matrix hardening is taken as the triaxiality limit where the damage mechanism shifts from

microvoid elongation to dilation. This triaxiality limit is referred to as the transition triaxiality limit,

which is taken as 0.75 in this thesis. In order to develop a computational fracture locus, it is

0

100

200

300

400

500

600

700

0.00 0.05 0.10 0.15 0.20 0.25

True stress(MPa)

Plastic strain

45

assumed that microvoid elongation and dilation are the only mechanisms of damage at low (less

than the transition triaxiality limit) and high triaxiality (larger than the transition triaxiality limit),

respectively.

For the low triaxiality regime (T ranges from zero to the transition limit), it is assumed that the

void elongation ratio reaches a critical value before the ligament between two neighboring

elongated microvoid fails (causing a local material to fracture). The critical value of void

elongation ratio is taken as 4 in this thesis.

For the high stress triaxiality regime, a rapid microvoid growth is observed at a certain

macroscopic effective plastic strain value. At this strain, the softening due to rapid microvoid

dilation dominates the matrix hardening leading to strain localization in the intervoid ligaments

resulting in overall softening behavior and finally leading to local material fracture.

In other words, for the fracture locus, in the low triaxiality regime the fracture strain increases

with the increase in triaxiality because the tendency of microvoids to elongate decreases with the

increase of the stress triaxiality. For high regime, the fracture strain decreases rapidly with the

increase of the stress triaxiality due to the fact that microvoids dilate rapidly at the high stress

triaxiality.

Figure 3.6 and 3.7 shows the evolution of stress triaxiality in the critical finite elements of the

shear tab (T95-45-1 and T95-45-2). The finite elements at which the failure initiated are referred

to as critical finite elements. Tables 3.4 and 3.5, Figures 3.8 and 3.9 show the calibration results

for T95 and T127 models.

critical element

46

Figure 3.6 Evolution of stress triaxiality in the critical finite element (bearing tear-out)

critical element

Figure 3.7 Evolution of stress triaxiality in the critical finite element (net-section rupture)

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0 2 4 6 8 10

Stress

triaxiality

Deformation (mm)

00.10.20.30.40.50.60.70.80.9

1

0 2 4 6 8 10

Stress

triaxiality

Deformation (mm)

Element removal

Element removal

47

Table 3.4 Calibration results of the fracture initiation for T95 models Fracture strain Stress triaxiality Strain rate 33.800 -0.333 0.010 27.780 -0.330 0.010 21.160 -0.325 0.010 13.780 -0.320 0.010 7.780 -0.312 0.010 2.240 -0.306 0.010 1.308 -0.297 0.010 0.824 -0.270 0.010 0.616 -0.235 0.010 0.500 -0.198 0.010 0.360 -0.166 0.010 0.320 -0.138 0.010 0.300 -0.118 0.010 0.280 -0.086 0.010 0.260 -0.050 0.010 0.220 0.000 0.010 0.226 0.105 0.010 0.254 0.265 0.010 0.260 0.290 0.010 0.266 0.333 0.010 0.300 0.480 0.010 0.340 0.610 0.010 0.400 0.750 0.010 0.300 1.000 0.010 0.200 1.400 0.010 0.130 2.000 0.010 0.100 3.000 0.010 0.080 4.000 0.010

Figure 3.8 Stress triaxiality vs. fracture strain for T95 models

0

0.2

0.4

0.6

0.8

1

-0.333 0.667 1.667 2.667 3.667

stress triaxiality vs fracture strain

48

Table 3.5 Calibration results of the fracture initiation for T127 models Fracture strain Stress triaxiality Strain rate 16.900 -0.333 0.010 13.890 -0.330 0.010 10.580 -0.325 0.010 6.890 -0.320 0.010 3.890 -0.312 0.010 1.120 -0.306 0.010 0.654 -0.297 0.010 0.412 -0.270 0.010 0.308 -0.235 0.010 0.265 -0.198 0.010 0.245 -0.166 0.010 0.234 -0.138 0.010 0.220 -0.118 0.010 0.210 -0.086 0.010 0.205 -0.049 0.010 0.200 0.000 0.010 0.205 0.105 0.010 0.225 0.265 0.010 0.240 0.333 0.010 0.310 0.480 0.010 0.460 0.666 0.010 0.595 0.780 0.010 0.380 1.000 0.010 0.150 1.500 0.010 0.110 2.000 0.010 0.090 3.000 0.010 0.080 4.000 0.010

Figure 3.9 Stress triaxiality vs. fracture strain for T127 models

0

0.2

0.4

0.6

0.8

1

-0.333 0.667 1.667 2.667 3.667

stress triaxiality vs fracture strain

49

For damage evolution, in the context of an elastic-plastic material with isotropic hardening, the

damage manifests itself in two forms: softening of the yield stress and degradation of the elasticity.

The solid curve in Figure 3.10 represents the damaged stress-strain response, while the dashed

curve is the response in the absence of damage.

Figure 3.10 Stress-strain curve with progressive damage degradation

In Figure 3.10, and are the yield stress and the equivalent plastic strain at the onset of

damage, and is the equivalent plastic strain at failure, at which the overall damage variable D

reaches the value of 1. The overall damage variable, D, captures the combined effect of all active

mechanisms and is computed in terms of individual damage variables, , for each mechanism.

The damage evolution is based on the effective plastic deformation (displacement at failure)

which is taken as 0.5mm herein, and once the damage initiation criterion has been reached, the

effective plastic displacement, , is defined with the evolution equation =L𝑝𝑙, where L is

the characteristic length of the element.

The evolution of the damage variable with the relative plastic displacement was specified in

linear form herein (Figure 3.11).

50

Figure 3.11 Definitions of damage evolution based on plastic displacement (linear)

The bolt and welded were regarded as elastic material with 200 GPa and 0.3 for Young’s

Modulus and Poisson’s ratio for the whole analysis

3.1.3 Assembly

In this step, all the parts which were created in the first step were moved into one coordinate system,

and then were combined into one model. Figures 3.12 shows the T95-45-1 model after assembling.

The bolt was put in the central of the hole (Figure 3.13), so it has a 0.8mm bolt slippage in the all

simulations.

Figure 3.12 The analysis model in Abaqus

51

Figure 3.13 The position of bolt

3.1.4 Setting analysis step

Abaqus provides the “step” for users to set analysis process. Each step can output any relative

variables by user’s setting. In this research, two general steps are employed: step 1 for elastic

analysis, and step 2 for plastic analysis. In each step, the software further employs many

incremental steps in the analysis automatically, and the maximum incremental step and

incremental size in each one can be set by users. Herein, 1000 and 1E-009 to 0.1 were used for

maximum incremental steps and the incremental size.

3.1.5 Applying interaction

In this part, the interaction properties and constraints can be applied for the model. The Abaqus

provides many contact interactions: general contact, surface-to-surface contact, self-contact, fluid

cavity, fluid exchange and so on. In this research, all the contact interactions were created as the

surface-to-surface contact. This type of contact uses finite sliding formulation which is based on a

master-slave contact pair algorithm. This algorithm can prohibit the nodes on the slave surface

from getting into the master surface, but allows the nodes on the master surface to get into the

slave surface. Therefore, it is important to select the proper surface type in the simulation.

According to Simulia (2011b), there are two rules for surface type selection: first, the slave surface

should be a surface with a finer mesh; second, the surface with softer material should be set as

slave surface if two surfaces’ mesh are similar.

For the interaction properties, friction was used in the modeling. The normal behavior was used

in the interaction properties, and the hard contact was chosen for pressure-overclosure which

created a contact constraint to surfaces and transferred the contact pressure between the two

surfaces if the clearance becomes zero. “Allow separation after contact” was used, and when the

52

contact pressure becomes zero or negative, this hard contact constraint was removed. The

tangential behavior was used with penalty friction formulation. This friction type controls the shear

stress transformation between the two surfaces. The tangential behavior occurred when the shear

stress reached a certain value and the slip appears between the two surfaces. Herein, the friction

coefficient was taken as 0.3.

The following three contacts with friction were used in the model:

1) the contact between the bolt surface and hole surface

2) the contact between the shear tab plate and the weld parts

3) the contact between the weld parts

For the constraint, “tie” and “coupling” were used in the modeling: the “tie” constraints were

for the surfaces of weld parts and shear plate, and the “coupling” was for the central point of the

circle surface of the bolt.

3.1.6 Applying load

In this part, boundary conditions and load were created. Four boundary conditions were built in

this model as follows:

1) the bottom surface of the model: U1= U2 = U3 = UR1 = UR2 = UR3 = 0

2) the cut surface of the shear plate (surface 1): U1 = UR2 = UR3 = 0

Figure 3.14 Surface 1

3) the cut surface of the shear plate (surface 2): U3 = UR1 = UR2 = 0

53

Figure 3.15 Surface 2

4) the cut surface of the bolt: U3 = UR1 = UR2 = 0

For the load, a displacement load was applied to the central point of the circle surface of the bolt

and acted on the coupling point which was created in the interaction part.

3.1.7 Mesh design

Mesh design is critical in the modelling, because it has major influence on the analysis results.

The first step of meshing was to partition each individual part, because the Abaqus could not fix

the complex geometry models. Then applying the seeds was used to determine the element size.

Next, choose the proper element type for each part. Last, choose the mesh type for meshing. Table

3.6 shows the details of meshing in each part.

Table 3.6 Mesh design of each part Part ID Element

code Shape Order Nodes

Size (mm)

Part 1 C3D8R Hexahedral Linear 8 2 Part 2 C3D8R Hexahedral Linear 8 2 Part 3 C3D8R Hexahedral Linear 8 2 Part 4 C3D4H Tetrahedron Linear 4 2 Part 5 C3D8R Hexahedral Linear 8 2

Note that for the element size, 4 mm was used at first to do the modeling, but the analysis results could not converge. Then, a smaller element size of 2 mm was used for modeling, and it gave a better result (computational time between 15-20 mins). For comparison, 1 mm element size was also used for modeling, and it had the same failure mode and similar load-deformation curve as the 2 mm element size model (but computational time was more than one hour). Therefore, 2 mm element size was chosen as the final element size for modeling.

3.1.8 Job

After all the defining parts, use “job” part to do the analysis, and it provides real time monitoring

during the analyzing.

54

3.1.9 Visualization

This part provides the display of the model and analysis results. Also, any variables and other result

information which are needed can be outputted in this section.

3.2 Simulation results

The following Figure 3.17 to Figure 3.26 show the load-deformation curves and deformation

shapes of the five simulations. Note that the deformation shapes shown by the figures are

corresponding to the red dots in the load-deformation curves.

The different colors on the final shape of simulations in this research represent the different

levels of stress at this moment, and the stress decreases with Figure 3.16 from left (red) to right

(blue). Note that all the Figures of deformations shape from Abaqus were used to check the failure

mode in this research, and the stresses were not concerned here.

Figure 3.16 Spectrum of stresses

Figure 3.17 Load-deformation curve of T95-45-1

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110

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Load (kN)

Deformation (mm)

T95-45-1

Figure 3.18a

Figure 3.18b

Figure 3.18c

55

(a) (b) First fracture (c)

Figure 3.18 Deformation shapes of T95-45-1


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Load (kN)

Deformation (mm)

T95-57-1

Figure 3.20b

Figure 3.20a Figure 3.20c

56

(a) (b) First fracture c

Figure 3.20 Deformation shape of T95-57-1



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T127-45-1

Figure 3.22

57



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Load (kN)

Deformation (mm)

T95-45-2

Figure 3.24

58



Table 3.7 Simulation results of lab tests Simulation ID Ty (kN) Rupture

deformation (mm) Failure mode

T95-45-1 368 19.1 Bearing tear-out T95-57-1 372 18.8 Net-section rupture T127-45-1 476 14.5 Bearing tear-out T95-45-2 444 10.5 Net-section rupture T127-45-2 604 10.6 Net-section rupture

Note: Ty definition is given in Chapter 5.

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Load (kN)

Deformation (mm)

T127-45-2

Figure 3.26

59

3.3 Comparison

Figure 3.27 to Figure 3.31 show the comparison of software and lab test curves of each specimen.

Figure 3.27 Specimen T95-45-1


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Deformation (mm)

T95-45-1 SoftwareLab test

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T95-57-1SoftwareLab test

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Deformation (mm)


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Deformation (mm)


61


3.4 Summary

Finite element models of lab test specimens were created through Abaqus to replicate the pure

tension tests. Table 3.8 shows the summary of the simulation results in comparison with the

predicted and test results.

By implementing the FE simulations strategy equipped with the ductile damage for metal model

and appropriate material properties, all the models succeeded in duplicating the failure modes of

bearing tear-out and net-section rupture of the tested shear tab connections.

Furthermore, the finite element models developed in this chapter can satisfactorily duplicate the

load-deformation curve of the specimens with one-column bolts only. However, more works need

to be done to improve the accuracy of the models corresponding to the two-column bolt specimens.

The work done in this chapter provides confidence for the author to conduct a parametric study

on the shear tab connections having one column bolts only in next chapter.

Table 3.8 Summary of the simulation results in comparison with the predicted and test results Specimen ID Predicted resistance

(kN) Test resistance (kN) FE simulation resistance

(kN) T95-45-1 110.75 104.75 106.00 T95-57-1 121.25 122.75 125.00 T127-45-1 144.50 130.75 140.00 T95-45-2 121.25 118.50 130.00 T127-45-2 160.75 157.00 175.00

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Load (kN)

Deformation (mm)


62

Chapter 4 Parametric study

In this chapter, the finite element models established in the previous chapter were used to conduct

a parametric study for the shear tabs having one column of bolts.

4.1 Parameters

The parameters of the shear tab connections are plate thickness, edge distance, bolt diameter and

shear load.

Three different plate thicknesses were considered: 6.4 mm, 9.5 mm and 12.7 mm; three different

bolt sizes were considered: diameter 19 mm, diameter 22.2 mm and diameter 25.4 mm; two

different edge distances were considered: 2.0d and 2.5d. For example, 45 mm and 57 mm for bolt

size of diameter 22.2 mm. In this way, 38 mm and 48 mm for bolt diameter 19 mm models, and

51mm and 64mm for bolt diameter 25.4 mm models; three different accompanied shear loads were

considered: V=0.15T, 0.30T, and 0.45T (d is bolt diameter, V is shear force, T is tension force).

Figure 4.1 shows how the shear load is applied.

4.2 Simulation results of 19mm bolt diameter

Figures 4.2 to 4.13 show load-deformation curves and the final deformed shapes of the six

simulations. Note that the material properties of the T64 models were taken the same as those of

the T95 models (see Chapter 3 for details).

is load orientation. when = 00, it is zero shear force or pure tension force; when = 900, it is pure shear force; when 00 900, it is combined tension and shear, T = P cos, V = P sin;

Figure 4.1 Combined tension and shear force

T P

V

63


Figure 4.3 Final deformed shape of T64-38-1

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70

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Load (kN)

Deformation (mm)

T64-38-1

64



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80

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Load (kN)

Deformation (mm)

T64-48-1

65



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90

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Load (kN)

Deformation (mm)

T95-38-1

66



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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Load (kN)

Deformation (mm)

T95-48-1

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Load (kN)

Deformation (mm)

T127-38-1

68



4.3 Simulation results of 22.2mm bolt diameter

Figures 4.14 to 4.19 show load-deformation curves and the final deformed shapes of the three

simulations.

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150

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Load (kN)

Deformation (mm)

T127-48-1

69



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80

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Load (kN)

Deformation (mm)

T64-45-1

70



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90

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Load (kN)

Deformation (mm)

T64-57-1

71



4.4 Simulation results of 23.8mm bolt diameter

Figures 4.20 to 4.31 show load-deformation curves and the final deformed shapes of the six

simulations.

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Load (kN)

Deformation (mm)

T127-57-1

72



0

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90

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Load (kN)

Deformation (mm)

T64-51-1

73



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90

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Load (kN)

Deformation (mm)

T64-64-1

74



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Deformation (mm)

T95-51-1

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Load (kN)

Deformation (mm)

T95-64-1

76



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160

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Load (kN)

Deformation (mm)

T127-51-1

77



4.5 Simulation results of combined tension and shear

Model T95-45-1 was used to do the simulation of combined tension and shear force. Due to the

existence of the shear load, the symmetry about axis 1 (Figure 3.2) is no longer valid. In order to

use the same one-quarter model, the constraints on the axis 1 surface were removed (Figures 4.33c,

4.33d and 4.33e) when V was not equal to zero, which allowed the plate to undergo deformation

in V direction. Figure 4.32 shows the load-deformation curves. Figure 4.33 shows the failure

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T127-64-1

78

modes of the 5 cases.

Figure 4.32 Load vs. deformation of T95-45-1 under combined tension and shear

(a) pure tension (experimental test) (b) pure tension (Abaqus)

(c) V=0.15T (Abaqus) (d) V=0.3T (Abaqus) (e) V=0.45T (Abaqus)

Figure 4.33 Failure modes of T95-45-1 under combined tension and shear

0

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80

90

100

110

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Load (kn)

Deformation (mm)

T95-45-1

pure tensionexperimental test

pure tension abaqus

V=0.15T abaqus

V=0.3T abaqus

V=0.45T

79

4.6 Observations

For the connections having 19 mm bolts, bearing tear-out was the only failure mode. For the other

connections, the failure mode mainly depended on the edge distance. When the edge distance was

2.5d, it had net-section rupture, and when the edge distance was 2d, it experienced a bearing tear-

out failure (Table 4.1).

When the shear load V was less than 0.45T, it had negligible influence on the results of the shear

tab connections, including the failure mode and the ultimate tensile strength.

Table 4.1 The summary of failure modes of the 18 simulations Thickness (mm) Bolt diameter (mm) Simulation ID Failure mode 6.4 19 T64-38-1 Bearing tear-out

T64-48-1 Bearing tear-out 22.2 T64-45-1 Bearing tear-out

T64-57-1 Net-section rupture 23.8 T64-51-1 Bearing tear-out

T64-64-1 Net-section rupture 9.5 19 T95-38-1 Bearing tear-out

T95-48-1 Bearing tear-out 22 T95-45-1 Bearing tear-out


T95-64-1 Net-section rupture 12.7 19 T127-38-1 Bearing tear-out

T127-48-1 Bearing tear-out 22 T127-45-1 Bearing tear-out


T127-64-1 Net-section rupture

80

Chapter 5 Analysis of the load versus deformation curve

In this chapter, a tri-linear load-deformation curve based on a three-stages of loading is developed.

5.1 The method of a tri-linear curve

The load-deformation curve of specimen T95-45-1 is used as an example for the explanation of

the proposed method hereafter.

Figure 5.1 Tri-linear curve of T95-45-1

0

10

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50

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80

90

100

110

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Load (kN)

Deformation (mm)

T95-45-1

B2

3

A

1

81

In Figure 5.1, a tri-linear curve, which is highlighted in red, is generated to replace the original

curve. This trilinear curve, representing the elastic, plastic and damage stages of the specimen, is

characterized by three critical points (Figure 5.2): effective yield tensile strength Ty and its

corresponding deformation Δy, ultimate tensile strength Tu and its corresponding deformation Δu,

residual strength Tr and its corresponding deformation Δr. Note that in this idealized tri-linear curve

bolt slippage is excluded. Thus, Δ𝑦 =𝑇𝑦

𝐾𝑦 , where Ky is the stiffness of the elastic stage. Three rules

are employed to generate the tri-linear curve: first, the area A above the actual curve should be

approximately equal to the area B below the actual curve; secondly, the effective elastic stiffness

Ky shall be taken as the secant stiffness calculated at a force equal to 60 percent of the effective

yield strength of the connection Ty; thirdly, the ultimate strength at the end of the plastic stage

should be between 0.95Tu to Tu (Tu is the ultimate strength of the original curve).

5.2 Determination of Ty and Δy

Six lab tests and fifteen simulations are used for the analysis. Table 5.1 records the deformation

values of Δy–Δb, Δu–Δb, and Δr–Δb, in which the bolt slippage deformation Δb is excluded from

the deformation data, corresponding to the Δy, Δu, and Δr in Figure 5.2. The effective yield strength

Ty and the effective elastic stiffness Ky, measured based on the procedure described in Section 5.1,

are also recorded in Table 5.1.

Figure 5.2 Load versus deformation of a nonlinear spring

Δ

T

Δr Δy Δu

Tu

Ty

Ky

Kp

Tr

82

Table 5.1 Summary of 6 lab tests and 15 simulations Specimen ID Δb

(mm) Δy–Δb

(mm) Δu–Δb (mm)

Δr–Δb (mm)

Ty for 2 bolts (N)

n t (mm) d (mm)

T95-45-1-a 0.9 2.3 13.2 17.3 384925 2 9.5 22.2 T95-45-1-b 1.7 2.3 12.9 17.6 382700 2 9.5 22.2 T95-57-1-a 1.5 2.7 14.9 17. 387150 2 9.5 22.2 T95-57-1-b 0.8 2.6 14.6 16.3 384925 2 9.5 22.2 T127-45-1-a 2.5 2.2 9.6 13.3 516200 2 12.7 22.2 T127-45-1-b 1.3 2.1 10.3 13.9 511750 2 12.7 22.2 T95-38-1 0.8 1.0 9.6 13.4 330000 2 9.5 19.0 T95-48-1 0.8 1.0 15.6 21.7 334000 2 9.5 19.0 T95-51-1 0.8 1.0 15.7 18.2 434000 2 9.5 23.8 T95-64-1 0.8 1.0 15.1 18.6 440000 2 9.5 23.8 T64-45-1 0.8 0.9 10.5 18.3 238000 2 6.4 22.2 T64-57-1 0.8 0.9 20.3 23.1 245000 2 6.4 22.2 T64-38-1 0.8 0.9 10.1 13.3 210000 2 6.4 19.0 T64-48-1 0.8 0.9 13.3 20.8 215000 2 6.4 19.0 T64-51-1 0.8 0.9 15.1 17.4 276000 2 6.4 23.8 T64-64-1 0.8 0.9 13.4 15.5 276500 2 6.4 23.8 T127-38-1 0.8 0.9 9.9 10.7 410000 2 12.7 19.0 T127-48-1 0.8 0.9 17.1 17.7 415500 2 12.7 19.0 T127-51-1 0.8 0.9 14.3 15.4 545000 2 12.7 23.8 T127-64-1 0.8 0.9 14.3 18.3 550000 2 12.7 23.8 T127-57-1 0.8 1.0 21.0 24.9 520000 2 12.7 22.2

83

Fu (MPa)

Fy (MPa)

𝑛𝑡 ⅆ𝐹𝑢 𝑛𝑡 ⅆ𝐹𝑦 𝑇𝑦

𝑛𝑡 ⅆ𝐹𝑢

𝑇𝑦

𝑛𝑡 ⅆ𝐹𝑦 Measured 𝐾𝑦 =

𝑇𝑦

Δ𝑦−Δ𝑏

for 2 bolts (N/mm) 𝐾𝑦

𝑡𝐹𝑦(ⅆ 25.4⁄ )

491 376 207103 158596 1.9 2.4 167358 53.6 491 376 207103 158596 1.8 2.4 166391 53.3 491 376 207103 158596 1.9 2.4 143388 45.9 491 376 207103 158596 1.9 2.4 148048 47.4 495 387 279402 218221 1.8 2.4 234636 54.6 495 387 279402 218221 1.8 2.3 243690 56.7 491 376 177251 135736 1.9 2.4 330000 123.5 491 376 177251 135736 1.9 2.5 334000 125.0 491 376 222030 170027 1.8 2.4 434000 121.5 491 376 222030 170027 1.9 2.4 440000 123.2 491 376 139522 106844 1.7 2.2 264444 125.7 491 376 139522 106844 1.8 2.3 272222 129.4 491 376 119411 91443 1.8 2.3 233333 129.6 491 376 119411 91443 1.8 2.4 238888 132.7 491 376 149578 114544 1.7 2.3 306666 127.4 491 376 149578 114544 1.7 2.3 307222 127.7 495 387 239128 186766 1.7 2.2 455555 124.0 495 387 239128 186766 1.7 2.2 461666 125.6 495 387 299539 233949 1.7 2.2 605555 123.0 495 387 299539 233949 1.7 2.2 611111 124.0 495 387 279402 218221 1.9 2.4 520000 121.0

Note: Δb is the bolt slippage; n is the number of bolts; t is the thickness of tab plate; d is bolt diameter.

(a) ntdFu vs Ty (b) ntdFy vs Ty

Figure 5.3 Determination of Ty

y = 1.84x

0

100000

200000

300000

400000

500000

600000

0 100000 200000 300000 400000

Ty (N)

𝑛𝑡 ⅆ𝐹𝑢

y = 2.37x

0

100000

200000

300000

400000

500000

600000

0 100000 200000

Ty (N)

84

Figure 5.4 Determination of Ky

The data points in Figure 5.4 are based on Abaqus models only; i.e., the data from the tested

specimens are not included in the regression analysis.

From Table 5.1, Figures 5.3 and 5.4, the effective yield tensile strength Ty and effective elastic

stiffness Ky can be obtained as:

𝑇𝑦 = 2.37𝑛𝑡 ⅆ𝐹𝑦 or (5.1)

𝑇𝑦 = 1.84𝑛𝑡 ⅆ𝐹𝑢 (5.2)

𝐾𝑦 = 124𝑡𝐹𝑦(ⅆ 25mm⁄ ) (5.3)

where n is the number of bolts; t is the thickness of tab plate; the bolt diameter d in Equation (5.3)

must be in unit of mm.

Note that the stiffness Ky of Equation (5.3) is based on the finite element models only. For the

tested 6 specimens, the average elastic stiffness is

𝐾𝑦𝑡 = 52𝑡𝐹𝑦(ⅆ 25mm⁄ ), (5.4)

This discrepancy is mainly attributed to the uneven bearing between the bolt shank and the tab

plate through the thickness direction and the deformation from the upper loading arm. The uneven

bearing was caused by: 1) the bending of the bolt shank, and 2) the imperfect fitting between the

shank and the hole, including that the hole surface was not flat due to punching and the bolts might

not come to bearing simultaneously.

Combining Equations (5.3) and (5.4) and considering the number of bolts, the effective elastic

stiffness Ky is obtained as

𝐾𝑦 = 62𝜆𝑛𝑡𝐹𝑦(ⅆ 25.4mm⁄ ) (5.5)

where 62 is equal to 124 divided by 2 bolts; λ is a calibration factor, which is equal to 0.42 for the

y = 124.22x

Measured Ky

tFy(d/25.4)

85

tested specimens, and is equal to 1.0 for the specimens of finite element models.

The effective yield deformation Δy is calculated as Ty/Ky, i.e.,

Δ𝑦 =2.37𝑛𝑡 ⅆ𝐹𝑦

62𝜆𝑛𝑡𝐹𝑦(𝑑 25mm⁄ )=

0.038ⅆ

𝜆(𝑑 25mm⁄ ) (5.6)

where (d/25mm) is the normalized dimensionless bolt diameter. Δy has the same unit as the d in

the numerator of the equation.

5.3 Determination of Tu and Δu

In this study, all the specimens were loaded to the rupture of shear tabs. The failure of the

connection is thus defined as various forms of rupture of steel materials. Note that the rupture

failure of bolts and welds were precluded from the test specimens through capacity design. In total,

there are three kinds of rupture modes.

1) Block shear failure. From the tests, it is possible to have tensile fracture across A-B before

rupture on the shear plane A-D and B-C, and this kind of failure is called block shear failure (Figure

5.5). The capacity can be obtained from the following equation:

T1 = [An Fu + 0.6 Agv (Fy + Fu) / 2] (5.7)

where An is net area; Fu is the ultimate strength of steel material; Agv is gross area in shear; and Fy

is yielding stress of steel material.

Figure 5.5 Block shear failure

2) Net-section rupture. This strength limit state is the rupture of steel material at the net section,

86

where the cross section is reduced by bolt holes. The strength equation is

T2 = An Fu (5.8)

where An is the net tensile area and Fu is the ultimate strength of steel material.

3) Bearing tear-out. In this case, a bolt bears against the edge of the hole. The bearing force is

limited by the shear strength of the hole edge (i.e. tear-out of the edge). The strength equation is

T3 = 0.6 [(Fy + Fu) / 2] Agv (5.9)

where Fy is yield strength of steel material; Fu is the ultimate strength of steel material; and Agv is

gross sectional area in shear, which is equal to the plate thickness times the sectional length in the

direction of the tear-out.

Table 5.2 and 5.3 show the calculation results of the 10 lab tests and 15 simulations. The

predicted strength of a connection is taken as the minimum value among the strengths obtained

from Equations (5.7), (5.8) and (5.9). It can be seen that the predicted strengths match the test

results very well.

Table 5.2 Calculation results of the 10 lab tests Specimen ID T95-45-1a T95-45-1b T95-57-1a T95-57-1b T127-45-1a t (mm) 9.41 9.41 9.38 9.44 12.43 L (mm) 152.30 152.63 152.24 152.55 152.08 l (mm) 76.11 76.35 75.72 75.76 75.50 c (mm) 45.19 45.63 57.68 56.97 43.90 dh (mm) 23.55 23.44 23.43 23.50 23.70 Fy (MPa) 376 376 376 376 387 Fu (MPa) 491 491 491 491 495 T1 (kN) 464 468 522 522 608 T2 (kN) 486 489 485 489 645 T3 (kN) 443 447 563 560 578 Tc (kN) 443 447 485 489 578 Tt (kN) 419 426 491 470 523 Tt/Tc 0.95 0.95 1.01 0.96 0.90

87

Specimen ID T127-45-1b T95-45-2a T95-45-2b T127-45-2a T127-45-2b t (mm) 12.33 9.38 9.37 12.39 12.38 L (mm) 151.71 152.48 152.27 152.09 152.08 l (mm) 75.42 75.29 75.50 75.31 74.75 c (mm) 43.99 121.14 121.65 121.16 121.18 dh (mm) 23.48 23.54 23.53 23.64 23.62 Fy (MPa) 387 376 376 387 387 Fu (MPa) 495 491 491 495 495 T1 (kN) 605 830 832 1112 1108 T2 (kN) 640 485 484 643 643 T3 (kN) 574 1183 1186 1590 1589 Tc (kN) 574 485 484 643 643 Tt (kN) 524 474 471 628 631 Tt/Tc 0.91 0.98 0.97 0.98 0.98

Note: t: plate thickness; L: plate length; l: distance between the two holes; c: edge distance, measured from the center of the bolt hole to the side edge; dh: bolt hole diameter; Tc: predicted ultimate tensile strength; Tt: ultimate tensile strength from the test; the number highlighted in yellow is the minimum of three failure modes

Table 5.3 Calculation results of the 15 simulations Specimen ID T95-38-1 T95-48-1 T95-51-1 T95-64-1 T64-45-1 t (mm) 9.50 9.50 9.50 9.50 6.40 L (mm) 152.00 152.00 152.00 152.00 152.00 l (mm) 76.00 76.00 76.00 76.00 76.00 c (mm) 38.00 48.00 51.00 64.00 45.00 dh (mm) 20.60 20.60 25.40 25.40 23.80 Fy (MPa) 376 376 376 376 376 Fu (MPa) 491 491 491 491 491 T1 (kN) 446 496 488 552 314 T2 (kN) 517 517 472 472 328 T3 (kN) 376 474 504 633 300 Tc (kN) 376 474 472 472 300 Tt (kN) 352 440 490 512 284 Tt/Tc 0.94 0.93 1.04 1.08 0.95

88

Specimen ID T64-57-1 T64-38-1 T64-48-1 T64-51-1 T64-64-1 t (mm) 6.40 6.40 6.40 6.40 6.40 L (mm) 152.00 152.00 152.00 152.00 152.00 l (mm) 76.00 76.00 76.00 76.00 76.00 c (mm) 57.00 38.00 48.00 51.00 64.00 dh (mm) 23.80 20.60 20.60 25.40 25.40 Fy (MPa) 376 376 376 376 376 Fu (MPa) 491 491 491 491 491 T1 (kN) 354 300 334 329 372 T2 (kN) 328 348 348 318 318 T3 (kN) 380 253 320 340 426 Tc (kN) 328 253 320 318 318 Tt (kN) 352 236 300 324 334 Tt/Tc 1.07 0.93 0.94 1.02 1.05

Specimen ID T127-38-1 T127-48-1 T127-51-1 T127-64-1 T127-57-1 t (mm) 12.70 12.70 12.70 12.70 12.70 L (mm) 152.00 152.00 152.00 152.00 152.00 l (mm) 76.00 76.00 76.00 76.00 76.00 c (mm) 38.00 48.00 51.00 64.00 57.00 dh (mm) 20.60 20.60 25.40 25.40 23.80 Fy (MPa) 387 387 387 387 387 Fu (MPa) 495 495 495 495 495 T1 (kN) 604 671 661 748 711 T2 (kN) 697 697 636 636 656 T3 (kN) 511 645 686 860 766 Tc (kN) 511 645 636 636 656 Tt (kN) 480 594 628 636 672 Tt/Tc 0.94 0.92 0.99 1.00 1.02

Note: t: plate thickness; L: plate length; l: distance between the two holes; c: edge distance, measured from the center of the bolt hole to the side edge; dh: bolt hole diameter; Tc: predicted ultimate tensile strength; Tt: ultimate tensile strength from the test; ; the number highlighted in yellow is the minimum of three failure modes

Therefore, the ultimate strength of a connection Tu is obtained as:

Tu = Min { T1, T2, T3 } (5.10)

Whether a connection fails by the rupture of net section or the bearing tear-out is dependent

upon which mode has a smaller tensile capacity. Using Equations (5.8) and (5.9), we can obtain

the following criterion for a net section rupture failure:

An Fu < 0.6 Agv (Fu + Fy )/ 2 (5.11)

where Agv=2ct for one bolt hole, and net area An=t(l – dh) for one bolt. Equation (5.11) is rewritten

as

89

𝑐

𝑑ℎ≥

1.67(𝑙

𝑑ℎ−1)

1+𝐹𝑦

𝐹𝑢

(5.12)

where l is the distance between the two holes or bolt pitch; dh is the hole diameter; c is the edge

distance.

For example, given t = 9.5 mm, dh = 23.8 mm, l = 76 mm, Fy = 376 MPa, Fu = 491MPa, we have

c/dh = 2.07. Table 5.4 shows value of c/dh from Equation (5.12) for 6 lab tests and 15 finite element

simulations. It can be seen that the equations correctly predict the failure modes.

Table 5.4 Determination of the ultimate deformation Specimen ID

Δu (mm)

Failure mode dh (mm)

d (mm)

Actual c/dh

Actual c/d

c/dh Eq.(5.12)

T95-45-1-a 13.2 B tear 23.8 22.20 1.89 2.03 2.07 T95-45-1-b 12.9 B tear 23.8 22.20 1.89 2.03 2.07 T95-57-1-a 14.9 N rupture 23.8 22.20 2.39 2.57 2.07 T95-57-1-b 14.6 N rupture 23.8 22.20 2.39 2.57 2.07 T127-45-1-a 9.6 B tear 23.8 22.20 1.89 2.03 2.05 T127-45-1-b 10.3 B tear 23.8 22.20 1.89 2.03 2.05 T95-38-1 9.6 B tear 20.6 19.00 1.84 2.00 2.54 T95-48-1 15.6 B tear 20.6 19.00 2.33 2.53 2.54 T95-51-1 15.7 B tear 25.4 23.80 2.00 2.14 1.88 T95-64-1 15.1 N rupture 25.4 23.80 2.52 2.69 1.88 T64-45-1 10.5 B tear 23.8 22.20 1.89 2.03 2.07 T64-57-1 20.3 N rupture 23.8 22.20 2.39 2.57 2.07 T64-38-1 10.1 B tear 20.6 19.00 1.84 2.00 2.54 T64-48-1 13.3 B tear 20.6 19.00 2.33 2.53 2.54 T64-51-1 15.1 B tear 25.4 23.80 2.00 2.14 1.88 T64-64-1 13.4 N rupture 25.4 23.80 2.52 2.69 1.88 T127-38-1 9.9 B tear 20.6 19.00 1.84 2.00 2.52 T127-48-1 17.1 B tear 20.6 19.00 2.33 2.53 2.52 T127-51-1 14.3 B tear 25.4 23.80 2.00 2.14 1.86 T127-64-1 14.3 N rupture 25.4 23.80 2.52 2.69 1.86 T127-57-1 21.0 N rupture 23.8 22.20 2.39 2.57 2.05

Note: l=76 mm for all the connections; Δu values exclude bolt slippage; B tear=bearing tear-out failure; N rupture=Net section rupture failure. The connections highlighted in yellow would have net section rupture failure based on Equation (5.12) criterion, but the finite element models predicted bearing tear-out failure.

90

(a) ∆u vs c/dh

(b) ∆u vs c/d

Figure 5.6 Determination of ∆u

From Table 5.4 and Figures 5.6, the ultimate deformation ∆u can be obtained as:

∆𝑢=6𝑐

𝑑ℎ+ 0.5 mm, or (5.13)

∆𝑢=5.5𝑐

𝑑+ 0.3 mm (5.14)

where c is edge distance, dh is bolt hole diameter; d is bolt diameter.

Note that the data of T64-57-1 and T127-57-1 were excluded in Figure 5.6. Table 5.5 shows the

calculation results of Equation (5.13) and (5.14).

y = 6x + 0.5

0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2 2.5 3

∆u (mm)

c/dh

y = 5.5x + 0.3

0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2 2.5 3

∆u (mm)

c/d

91

Table 5.5 Calculation results of Equation (5.13) and (5.14) Specimen ID Δu

(mm) Actual c/dh

Actual c/d

Eq.(5.13) (mm)

Eq.(5.13)/Δu

Eq.(5.14) (mm)

Eq.(5.14)/Δu

T95-45-1-a 13.2 1.89 2.03 11.84 0.90 11.47 0.87 T95-45-1-b 12.9 1.89 2.03 11.84 0.92 11.47 0.89 T95-57-1-a 14.9 2.39 2.57 14.84 1.00 14.44 0.97 T95-57-1-b 14.6 2.39 2.57 14.84 1.02 14.44 0.99 T127-45-1-a 9.6 1.89 2.03 11.84 1.23 11.47 1.19 T127-45-1-b 10.3 1.89 2.03 11.84 1.15 11.47 1.11 T95-38-1 9.6 1.84 2.00 11.54 1.20 11.30 1.18 T95-48-1 15.6 2.33 2.53 14.48 0.93 14.22 0.91 T95-51-1 15.7 2.00 2.14 12.50 0.80 12.07 0.77 T95-64-1 15.1 2.52 2.69 15.62 1.03 15.10 1.00 T64-45-1 10.5 1.89 2.03 11.84 1.13 11.47 1.09 T64-57-1 20.3 2.39 2.57 14.84 0.73 14.44 0.71 T64-38-1 10.1 1.84 2.00 11.54 1.14 11.30 1.12 T64-48-1 13.3 2.33 2.53 14.48 1.09 14.22 1.07 T64-51-1 15.1 2.00 2.14 12.50 0.83 12.07 0.80 T64-64-1 13.4 2.52 2.69 15.62 1.17 15.10 1.13 T127-38-1 9.9 1.84 2.00 11.54 1.17 11.30 1.14 T127-48-1 17.1 2.33 2.53 14.48 0.85 14.22 0.83 T127-51-1 14.3 2.00 2.14 12.50 0.87 12.07 0.84 T127-64-1 14.3 2.52 2.69 15.62 1.09 15.10 1.06 T127-57-1 21.0 2.39 2.57 14.84 0.71 14.44 0.69

Note: l=76 mm for all the connections; Δu values exclude bolt slippage.

From Table 5.5, the predicted ultimate deformation Δu of a connection from Equations (5.13)

and (5.14) are acceptable comparing with the Δu from test or model.

5.4 Determination of Tr and Δr

From Table 5.6 and Figure 5.7, the residual strength Tr of a connection can be obtained

approximately as:

𝑇𝑟 = 0.7𝑇𝑢 (5.15)

92

Table 5.6 Determination of Tr Specimen ID d

(mm) Tu for 2 bolts

(N) Tr for 2 bolts

(N) Eq.(5.15)

(N) Eq.(5.15)/ Tr

T95-45-1-a 22.20 385000 258100 269500 1.04 T95-45-1-b 22.20 386000 262550 270200 1.03 T95-57-1-a 22.20 440000 302600 308000 1.02 T95-57-1-b 22.20 426000 289250 298200 1.03 T127-45-1-a 22.20 476000 347100 333200 0.96 T127-45-1-b 22.20 474000 373800 331800 0.89 T95-38-1 19.00 352000 258100 246400 0.95 T95-48-1 19.00 440000 298150 308000 1.03 T95-51-1 23.80 490000 338200 343000 1.01 T95-64-1 23.80 512000 311500 358400 1.15 T64-45-1 22.20 284000 231400 198800 0.86 T64-57-1 22.20 352000 235850 246400 1.04 T64-38-1 19.00 236000 169100 165200 0.98 T64-48-1 19.00 300000 258100 210000 0.81 T64-51-1 23.80 324100 280350 226870 0.81 T64-64-1 23.80 334000 255875 233800 0.91 T127-38-1 19.00 480000 448000 336000 0.75 T127-48-1 19.00 594100 556000 415870 0.75 T127-51-1 23.80 628000 544000 439600 0.81 T127-64-1 23.80 636100 467250 445270 0.95 T127-57-1 22.20 672000 502850 470400 0.94

Figure 5.7 Determination of Tr

y = 0.7x

0

100000

200000

300000

400000

500000

600000

700000

0 100000 200000 300000 400000 500000 600000 700000 800000

Tr (N)

Tu (N)

93

Table 5.7 Determination of Δr

Specimen ID Δr (mm)

Actual c/dh

Actual c/d

Eq.(5.16) (mm)

Eq.(5.16)/Δr

Eq.(5.17) (mm)

Eq.(5.17)/Δr

T95-45-1-a 17.3 1.89 2.03 16.01 0.93 15.73 0.91 T95-45-1-b 17.6 1.89 2.03 16.01 0.91 15.73 0.89 T95-57-1-a 17.0 2.39 2.57 18.26 1.07 18.05 1.06 T95-57-1-b 16.3 2.39 2.57 18.26 1.12 18.05 1.11 T127-45-1-a 13.3 1.89 2.03 16.01 1.20 15.73 1.18 T127-45-1-b 13.9 1.89 2.03 16.01 1.15 15.73 1.13 T95-38-1 13.4 1.84 2.00 15.78 1.18 15.60 1.16 T95-48-1 21.7 2.33 2.53 17.99 0.83 17.88 0.82 T95-51-1 18.2 2.00 2.14 16.50 0.91 16.20 0.89 T95-64-1 18.6 2.52 2.69 18.84 1.01 18.57 1.00 T64-45-1 18.3 1.89 2.03 16.01 0.87 15.73 0.86 T64-57-1 23.1 2.39 2.57 18.26 0.79 18.05 0.78 T64-38-1 13.3 1.84 2.00 15.78 1.19 15.60 1.17 T64-48-1 20.8 2.33 2.53 17.99 0.86 17.88 0.86 T64-51-1 17.4 2.00 2.14 16.50 0.95 16.20 0.93 T64-64-1 15.5 2.52 2.69 18.84 1.22 18.57 1.20 T127-38-1 10.7 1.84 2.00 15.78 1.47 15.60 1.46 T127-48-1 17.7 2.33 2.53 17.99 1.02 17.88 1.01 T127-51-1 15.4 2.00 2.14 16.50 1.07 16.20 1.05 T127-64-1 18.3 2.52 2.69 18.84 1.03 18.57 1.01 T127-57-1 24.9 2.39 2.57 18.26 0.73 18.05 0.72

Note: l=76 mm for all the connections; Δr values exclude bolt slippage.

(a) ∆r vs. c/dh

y = 4.5x + 7.5

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3

∆r (mm)

c/dh

94

(b) ∆r vs. c/d

Figure 5.8 Determination of Δr

From Table 5.7 and Figure 5.8, deformation Δr of a connection can be calculated as:

𝛥𝑟 =4.5𝑐

𝑑ℎ+ 7.5 mm, or (5.16)

∆𝑟=4.3𝑐

𝑑+ 7 mm (5.17)

From the calculation results in Tables 5.5 and 5.6, the predicted residual strength Tr from

Equation (5.15) and its corresponding deformation Δr from Equations (5.16) and (5.17) are

acceptable comparing with the Tr and Δr from the test or finite element models.

y = 4.3x + 7

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3

∆r (mm)

c/d

95

Chapter 6 Conclusions and future works

This chapter summarizes the research work of this thesis and provides some recommendations for

future studies.

6.1 Summary and conclusions

This thesis consists of four parts: lab test, finite element modeling, parametric study, and load-

deformation curve.

First, the test of two series of coupons and ten shear tab connections under a pure tension load

were performed. The coupon test results included the material properties such as yield strength,

ultimate strength and necking initiation strain. The shear tab connection test results included the

failure modes and the load-deformation curves.

Second, software Abaqus was used to simulate the pure tension test of the shear tab connections.

The test load-deformation curves and failure modes were used to calibrate the finite element

models.

Third, the verified finite element models were employed to conduct a parametric study. Four

parameters, i.e., plate thickness, edge distance, bolt diameter and shear load, were studied, which

resulted in 15 simulations.

Last, a tri-linear curve was developed to predict the load versus deformation relationship of a

shear tab connection having one-column bolts.

The following conclusions can be drawn from this research work:

1) Tensile rupture of the net section and bearing tear-out of the bolt hole side edge were the

typical failure modes of the tested shear tab connections, for which the rupture of bolts or welds

was precluded by a capacity design principle.

2) All the connections exhibited good ductility, i.e., experienced large plastic deformation before

a rupture failure.

3) When the accompanying shear load was less than 45 percent of the tensile load, the impact

of the shear load on the tensile strength and the tensile deformation of the shear tab connections

could be ignored.

4) The actual load-deformation curves of the shear tab connections could be represented by a

tri-linear curve, whose values at the three critical points are given by Equations (5.1) and (5.6),

96

Equations (5.10) and (5.14), and Equations (5.15) and (5.17), respectively.

Note that the developed tri-linear curve is valid under the following assumptions: (1) the bolt

size ranges from 19 mm (3/4 in) to 25 mm (1 in); (2) the tab plate thickness ranges from 6.4 mm

(1/4 in) to 12.7 mm (1/2 in); (3) the side edge distance of bolt holes ranges from 2 to 2.5 of the

bolt diameter; (4) the pitch of the bolts is 76 mm (3 in); and (5) the distance between the boltline

and the weldline is 80 mm.

6.2 Future works

The finite element models for the shear tab connections having two-column bolts need to be

further calibrated to achieve a satisfactory accuracy.

When the shear load V was larger than 0.45T, the preliminary simulation showed different

failure modes (Figure 6.1), which could be investigated further.

A parametric study including bolt pitch and the distance between the boltline and the weldline

should be conducted in a future study.

(a) (b)

Figure 6.1 Failure modes when V 0.45T

97

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